324.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 324

Reference: erdosproblems.com/324

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

theorem Erdos324.erdos_324 Does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ such that all the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct? sorry line 37 source
Source documentation
Does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ such that all the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct?

depends on sorry what this means
Statement uses: Iff, True, Exists, Polynomial, Int, Set.InjOn, Prod, Nat, Erdos324.erdos_324.match_1, HAdd.hAdd, Polynomial.eval, Set.ofPred, LT.lt
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
13 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_324 : answer(sorry) ↔
    ∃ f : ℤ[X], {(a, b) : ℕ × ℕ | a < b}.InjOn fun (a, b) => f.eval (a : ℤ) + f.eval (b : ℤ) := by
…
```
theorem Erdos324.erdos_324.variants.quintic Probably $f(x) = x^5$ has the property that the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct sorry line 46 source
Source documentation
Probably $f(x) = x^5$ has the property that the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct.

depends on sorry what this means
Statement uses: Set.InjOn, Prod, Nat, Erdos324.erdos_324.match_1, HAdd.hAdd, HPow.hPow, OfNat.ofNat, Set.ofPred, LT.lt
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_324.variants.quintic : {(a, b) : ℕ × ℕ | a < b}.InjOn fun (a, b) => a ^ 5 + b ^ 5 := by
…
```